Zorich [1]} introduced an
important example of a quasiregular self-map of \(\mathbb {R}^3\) 
which can be considered as a 3-dimensional analogue of the exponential
function.
In fact, the construction is quite flexible and
also works in \(\mathbb {R}^d\)  for all \(d\ge 2\) ;
see [2]}.
We follow [3]} in the definition of a Zorich map
and consider the cube
\(Q:=\left\lbrace x\in \mathbb {R}^{d-1}\colon \Vert x\Vert _\infty \le 1\right\rbrace =[-1,1]^{d-1}\) 
